Quote
Originally posted by: crapshooter
MoneyLA
I apologize if this sounds redundant because I chose not to read 3 pages of bantering...
Here's the way I see it. Your friend is looking to maximize the ability to earn tier points with minimum effect on his bankroll.
You list 33.8% chance of a winning hand by holding a jack (about 1 in 3) vs. 28.7% with deuces (slightly more than 1 in 4).
However, I think it is better to list what the chances are of hitting a J by holding a J vs. hitting another 2 by holding the deuces. (for our sakes and purposes, I think it would be safe to assume the same proportional ratio of 1/3 for the Jack, and 1/4 for the deuces) Yes...you can't hit a royal holding the deuces, but you can't hit trip or quad deuces holding just the jack (because you'd be discarding 2 deuces)
Once again, I am keeping the idea of earning points in mind over proper strategy.
Yes, proper strategy dictates you keep the 2's
I will keep this in perspective of betting units (I will explain later on)
Thus, if your friend gets 60 hands of J 2 2 10 5. If the Jack was kept, 20 out of the 60 hands would pay even money. The rest would be lost. So 300 units wagered (5 units per draw, 30 draws), 20 hands pay even money, therefore, 100 units would return and 200 units lost.
Same 10 hands, but deuces are kept. If the 2 is kept instead of the Jack, then 15 hands would pay out. But it would pay out 15 units per hand. So, 300 units wagered, 15 hands won, 15 credits per winning hand, therefore 225 units won and 75 units lost.
Based on this analysis it pays to keep the deuce, even if the proportion was changed from 1/4 to 1/6, it still makes sense to play the deuces.
The last step is determining long term vs. short term. What denomination is being played? $1, $5, $100, $5,000?? In other words, if I play high denomination VP, I may not be looking for long term variance. If I was playing $5,000 per unit at max ($25,000 per dealt hand), and I was dealt J 2 2 10 5, I would be holding the Jack.
However, I don't think your friend would be playing that level. So I think it's still safe to say that correct strategy is the proper play. Only because it takes into account the rewards vs. the risk.
Sorry for the lengthy reply
-Shooter
By holding the J alone, you also get shots at a flush or a straight. Not so with holding a pair. Yes, by throwing away the pair of dueces you ruin any shot at trip or quad deuces but you open up other possibilities.
The stat referenced said you had a 33.8 % chance of a winning hand. You seem to be factoring in only a pair of jacks as the possible winning hand. It's quite possible I'm misinterpreting your post, if so please let me know.